2y(y+6)=32

Solution for 2y(y+6)=32 equation:

Simplifying
2y(y + 6) = 32

Reorder the terms:
2y(6 + y) = 32
(6 * 2y + y * 2y) = 32
(12y + 2y2) = 32

Solving
12y + 2y2 = 32

Solving for variable 'y'.

Reorder the terms:
-32 + 12y + 2y2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 12y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 6y + y2) = 0

Factor a trinomial.
2((-8 + -1y)(2 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-8, 2}